The qualitative properties of an open magnetosphere and its electric field are examined and compared to a simple model of a dipole in a constant field and to actual observations. Many of these properties are found to depend on the separatrix, a curve connecting neutral points and separating different field-line regimes. In the simple model, the electric field in the central polar cap tends to point from dawn to dusk for a wide choice of external fields. Near the boundary of the polar cap electric equipotentials curve and become crescent-shaped, which may explain the correlation of polar magnetic variations with the azimuthal component of the interplanetary magnetic field, reported by Svalgaard. Modifications expected to occur in the actual magnetosphere are also investigated: in particular, it appears that bending of equipotentials may be reduced by cross-field flow during the merging of field lines and that open field lines connected to the polar caps emerge from a long and narrow slot extending along the tail.